Question

Consider circle T with radius 24 in. and θ = StartFraction 5 pi Over 6 EndFraction radians. Circle T is shown. Line segments S T and V T are radii with lengths of 24 inches. Angle S T V is theta. What is the length of minor arc SV?

Answer 1

20 pi

Explanation:

Answer 2

20π in

Explanation:

Length of an arc is expressed as
`L = (\theta)/(2\pi ) * 2\pi r\\`. Given;

`\theta = (5\pi )/(6) rad\\ radius = 24in\\`

The length of the minor arc SV is expressed as:

`L = ((5\pi )/(6) )/(2\pi ) * 2\pi (24)\\L = (5\pi )/(12\pi ) * 48\pi \\L = (5)/(12) * 48\pi \\L = (240\pi )/(12) \\L = 20\pi \ in`

Hence, The length of the arc SV is 20π in